For (2) you are fine until you get to $\displaystyle k^2+ 3k+ 2$ and there you stop. Don't forget what you are trying to prove. You want to prove that sum is n(n+1) which, for n= k+1, is (k+1)(k+2). Factor $\displaystyle k^2+ 3k+ 2$!

For (3), $\displaystyle (2x+3y)^4$ has mysteriously become $\displaystyle (3x+ 3y)^4$!